Question

Two masses hang freely over a pulley. Their masses are 6.5 kg and 11 kg. Find the acceleration of each mass and the tension in the rope if friction is neglected.

Answer 1

Accleration of masses =
`2.522m/s^(2)`

Tension in rope = 80.158 Newtons

Step-by-step explanation:

Applying Newtons second law to both the masses we have

For 6.5 kg mass we have

`T_(1)-6.5* g=6.5* a_(1)...................(i)`

Similarly for 11 kg mass applying Newton's second law yields

`11* g-T_(2)=11* a_(1)...............(ii)`

Now since both the masses are connected by same string and the pulley is friction less the acceleration of both the masses shall be same and the tension in the string shall have unique value

thus solving equation i and ii by adding them we get

`11g-6.5g=6.5a+11a\\\\\therefore a=(11g-6.5g)/(11+6.5)=0.257g\\\\a=0.257* 9.81m/s^(2)=2.522m/s^(2)`

Using this value of accleration in any equation we obatin the value of tension as

`T=6.5a+6.5g\\\\\therefore T=80.158Newtons`